compression of breast cancer images by principal component analysis

Authors

monika saraswat

a. k. wadhwani

manish dubey

abstract

the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in matrix form as ui∈ rr ×c,  i = 1,......,n, where r and c are, repetitively, the number of rows and columns of the matrix. in vectorized representation (matrix-to-vector alignment) each ui is a n = r × c- dimensional vector ai computed by sequentially concatenating all of the lines of the matrix ui. to compute the principal components the covariance matrix of u is formed and eigen values, with the corresponding eigenvectors, are evaluated. the eigen vectors forms a set of linearly independent vectors, i.e., the base {φ} n i=1 which consist of a new axis system [10]

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Journal title:
international journal of advanced biological and biomedical research

Publisher: casrp publishing company

ISSN 2383-2762

volume 1

issue 7 2013

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